(Bloomberg) Senate Majority Leader Harry Reid rejected the latest Republican offer to resolve the U.S. fiscal crisis as Minority Leader Mitch McConnell reached out to Vice President Joe Biden in an effort to break the impasse.

“The sticking point appears to be a willingness or interest or frankly, the courage to close the deal,” McConnell, a Kentucky Republican, said on the Senate floor Sunday. “I’m willing to get this done, but I need a dance partner.”

Senator John McCain of Arizona said his fellow Republicans will stop insisting on using a new inflation measure that would lead to smaller Social Security cost-of-living increases.

“It’s not a winning argument to say benefits for seniors versus tax breaks for rich people,” McCain told reporters.

Reid said earlier today that Democrats wouldn’t agree to use the new inflation measure as part of a short-term deal. He said he would keep trying to come up with an offer to Republicans.

“We’re making progress. At this stage we don’t have a deal, and that’s an understatement,” said Reid, a Nevada Democrat.

Congress is working to avert more than $600 billion in tax increases and federal spending cuts, the so-called fiscal cliff, set to start taking effect in two days. The House and Senate are holding an unusual Sunday session after President Barack Obama on Dec. 28 asked Reid and McConnell to try to find a solution.

Regarding talks between McConnell and Biden, Reid said, “I wish them well.” Biden is at the White House, according to an administration official who spoke on condition of anonymity.

‘Adverse Reaction’
During an interview broadcast earlier today on NBC’s “Meet the Press,” Obama made a last-minute appeal for compromise and warned of “an adverse reaction in the markets” if Congress doesn’t act.

Republicans “say that their biggest priority is making sure that we deal with the deficit in a serious way, but the way they’re behaving is that their only priority is making sure that tax breaks for the wealthiest Americans are protected,” Obama said. He said his offers to Republicans have been “so fair that a lot of Democrats get mad at me.”

In a statement, House Speaker John Boehner, an Ohio Republican, called Obama’s comments “ironic, as a recurring theme of our negotiations was his unwillingness to agree to anything that would require him to stand up to his own party.”

The setback follows 24 hours of progress toward a deal, according to a Democratic aide familiar with the talks. During the previous two days, Reid and McConnell had been closing in on agreement on a threshold for letting income tax rates increase for top earners and narrowing differences over the estate tax, the aide said.

Bush-Era Cuts
Republicans and Democrats agree that George W. Bush-era income tax cuts should be extended for the vast majority of taxpayers. Obama and other Democrats want to let the tax cuts expire for the top 2 percent, or married couples earning more than $250,000 a year. Republicans oppose higher tax rates for any income level.

In the event the Senate can’t reach a compromise, Obama has asked Reid to ready a bare-bones bill for a vote by Monday to extend expanded unemployment benefits and tax cuts on family income up to $250,000.

In that scenario, Obama said on NBC, “Republicans will have to decide if they’re going to block it, which will mean that middle-class taxes do go up.” Any compromise needs to be passed by the Republican-controlled House of Representatives.

Today marks the first time since Oct. 29, 2000, that both the House and Senate are casting votes on a Sunday, according to congressional records. The House has met on 16 Sundays since World War II, according to records of the House clerk and historian’s offices.

Still Optimistic
New York Senator Charles Schumer, the chamber’s third- ranking Democrat, told reporters on his way into a closed-door party meeting that he was still optimistic a deal could happen before year’s end.

“They always happen at the end; that’s how I’ve seen it happen all along,” Schumer said.
Democrats have insisted that the co-called chained CPI inflation yardstick, which would trim Social Security cost-of- living increases, must be accompanied by a multiyear increase in the U.S. debt ceiling. The Republican-run House has used its authority over raising the debt ceiling to extract spending cuts from Democrats.

Obama agreed earlier this month to consider the new inflation gauge during budget negotiations with House Speaker John Boehner. After those talks halted, the focus has narrowed to a scaled-back plan in which Democrats and some Republicans say chained CPI has no place.

‘Not Crucial’
“That to me is not crucial at all, not at all at this stage,” said South Carolina Senator Lindsey Graham, a Republican.

Senator Dan Coats, an Indiana Republican, concurred. Once the tax issue is resolved, then Congress will begin to deal with spending, “and that’s when chained CPI and entitlement reform and tax reform and a whole number of other things come into play.”

Markets dropped last week as the stalemate continued. The Standard & Poor’s 500 Index fell for a fifth day on Dec. 28, by 1.1 percent to 1,402.45 at the 4 p.m. close in New York. The benchmark Treasury 10-year yield declined four basis points, or 0.04 percentage point, to 1.7 percent at 5 p.m. in New York, according to Bloomberg Bond Trader.

If Congress does nothing, taxes will rise in 2013 by an average of $3,446 for U.S. households, according to the nonpartisan Tax Policy Center in Washington.

Delayed Tax Filing
Tax filing for as many as two-thirds of U.S. taxpayers could be delayed into at least late March. Defense spending would be cut, and the economy would probably enter a recession in the first half of 2013, according to the Congressional Budget Office.

The effects of the higher tax rates and federal spending cuts would accumulate over a matter of months. Congress could reverse them by acting retroactively in 2013.

The current state of talks isn’t necessarily ominous, said Senator Olympia Snowe of Maine, a Republican.

“The one thing Congress is predictable about, and that is waiting until the very last hour, and maybe it is going to be the eleventh hour,” she said. “We got one more day.”

—With assistance from James Rowley, Margaret Talev, Richard Rubin and Roxana Tiron in Washington. Editors: Laurie Asseo, Jodi Schneider